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by: Aric Jast MD


Aric Jast MD
GPA 3.52


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Class Notes
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This 5 page Class Notes was uploaded by Aric Jast MD on Thursday September 17, 2015. The Class Notes belongs to EML 3002C at Florida State University taught by Staff in Fall. Since its upload, it has received 82 views. For similar materials see /class/205484/eml-3002c-florida-state-university in Engineering Mechanical at Florida State University.


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Date Created: 09/17/15
The Carnot Cycle 39 Idealized thermodynamic cycle consisting of four reversible processes any substance gt Reversible isothermal expansion 12 THconstant gt Reversible adiabatic expansion 23 QO TH TL gt Reversible isothermal compression 34 TLconstant gt Reversible adiabatic compression 41 QO TL TH ls therlnal Adia bafic Isothermal Ad iabatiF expansmn BXPanston compression compressmquot The Carnot Cycle2 FIGURE 544 P v diagram of the Carnot cycle Net work 2 Work done by gas JPdV area under the process curve 123 1 dVgtO from 123 2 JPdVgt0 7 Work done on gas JPdV area under the process curve 341 subtract 1 Since dVltO JPdVlt0 The Carnot Principles 39 The ef ciency of an irreversible heat engine is always less than the ef ciency of a reversible one operating between the same two reservoirs nth irrev lt nth rev 0 The ef ciencies of all reversible heat engines operating between the same two reservoirs are the same nth reVA 11mmB 0 Both Can be demonstrated using the second law KP statement and C statement Therefore the Carnot heat engine de nes the maximum ef ciency any practical heat engine can reach up to 0 Thermal ef ciency nthWnetQH1QLQHfTLTH and it can be shown that nth1QLQH1TLTH This is called the Carnot ef ciency 0 For a typical steam power plant operating between TH800 K boiler and TL300 Kcooling tower the maximum achievable ef ciency is 625 Example Let us analyze an ideal gas undergoing a Carnot cycle between two temperatures TH and TL gt 1 to 2 isothermal expansion AU12 0 QH Q12 w12 JPdV mRTH1nV2V1 gt 2 to 3 adiabatic expansion Q23 0 TLTH VzV3k1 9 1 gt 3 to 4 isothermal compression AU34 0 QL Z Q34 2 W34 2 39 mRTLlnV4V3 gt 4 to 1 adiabatic compression Q41 0 TLTH V1V4k1 9 2 From 1 amp 2 V2N3 V1V4 and VZVl V3V4 nth 139QLQH 2 139TLTH Since 1nV2V1 1nV4V3 It has been proven that nth 1QLQH lTLTH for all Carnot engines since the Carnot ef ciency is independent of the working substance Carnot Ef ciency A Carnot heat engine operating between a hightemperature source at 900 K and reject heat to a lowtemperature reservoir at 300 K a Determine the thermal ef ciency of the engine b If the temperature of the high temperature source is decreased incrementally how is the thermal ef ciency changes with the temperature 1 I I I 08 Lower T T 300 e H nthI Ll O667667 E 06 7 900 a ThltTgt 0 4 Fixed TL 2 300K and lowering TH 02 0 T 1 200 400 600 800 1000 nm H 7 T T TH emperature The higher the temperature the higher the quality 1 I I of the energy More work can be done 08 39 Increase TL 06 THTL 04 Ef ciency Fixed TH 900K and increasing TL 02 T T 1 L o m 900 200 400 600 800 1000 TL Temperature TL


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